基于公交上下车计数的时变起讫点矩阵贝叶斯推断
Bayesian Inference of Time-Varying Origin-Destination Matrices from Boarding/Alighting Counts for Transit Services
AI总结：
针对公交系统设计运营所需的OD需求矩阵，提出一种时间贝叶斯模型，通过分解潜在变量矩阵减少参数并施加高斯过程先验，采用两阶段MCMC算法推断，在真实数据上优于IPF且能量化不确定性。
摘要：
起讫点（OD）需求矩阵对公交机构设计和运营公交系统至关重要。本文提出一种新颖的时间贝叶斯模型，旨在从公交站点的上下车计数中估计单个公交行程层面的公交OD矩阵。我们的方法首先通过以下车概率为参数的多项分布，对给定上车站点时后续公交站点的下车乘客数量进行建模。考虑到问题的大规模性，我们用一个潜在变量矩阵生成下车概率，并将其分解为映射矩阵和时间矩阵，从而大幅减少参数数量。为进一步在参数中编码时间平滑结构，我们对时间因子矩阵的列施加高斯过程先验。对于模型推断，我们开发了一种基于马尔可夫链蒙特卡罗（MCMC）方法的两阶段算法。第一阶段，使用带有基于马尔可夫模型的提议分布的Metropolis-Hastings抽样算法，在给定模型参数的条件下对潜在OD矩阵进行抽样。第二阶段，使用切片和椭圆切片抽样算法，在给定潜在OD矩阵的条件下对模型参数进行抽样。我们使用从三条具有不同站点数量的公交线路收集的真实世界数据评估所提出的模型，结果表明我们的模型实现了准确的后验均值估计，并优于广泛使用的迭代比例拟合（IPF）方法。此外，我们的模型可以为OD需求矩阵提供不确定性量化，从而有利于许多需要稳健决策的下游规划/运营任务。
英文摘要：
Origin-destination (OD) demand matrices are crucial for transit agencies to design and operate transit systems. This paper presents a novel temporal Bayesian model designed to estimate transit OD matrices at the individual bus-journey level from boarding/alighting counts at bus stops. Our approach begins by modeling the number of alighting passengers at subsequent bus stops, given a boarding stop, through a multinomial distribution parameterized by alighting probabilities. Given the large scale of the problem, we generate alighting probabilities with a latent variable matrix and factorize it into a mapping matrix and a temporal matrix, thereby substantially reducing the number of parameters. To further encode a temporally-smooth structure in the parameters, we impose a Gaussian process prior on the columns of the temporal factor matrix. For model inference, we develop a two-stage algorithm with the Markov chain Monte Carlo (MCMC) method. In the first stage, latent OD matrices are sampled conditional on model parameters using a Metropolis-Hastings sampling algorithm with a Markov model-based proposal distribution. In the second stage, we sample model parameters conditional on latent OD matrices using slice and elliptical slice sampling algorithms. We assess the proposed model using real-world data collected from three bus routes with varying numbers of stops, and the results demonstrate that our model achieves accurate posterior mean estimation and outperforms the widely used iterative proportional fitting (IPF) method. Additionally, our model can provide uncertainty quantification for the OD demand matrices, thus benefiting many downstream planning/operational tasks that require robust decisions.
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